Empirical Tests on the Validity of Asset Pricing Models

James W. Kolari (), Wei Liu, Jianhua Z. Huang () and Huiling Liao ()
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James W. Kolari: Texas A&M University, Mays Business School
Wei Liu: Texas A&M University, Mays Business School
Jianhua Z. Huang: The Chinese University of Hong Kong, Shenzhen, School of Artificial Intelligence and School of Data Science
Huiling Liao: Illinois Institute of Technology, Department of Applied Mathematics

Chapter Chapter 7 in Asset Pricing Models and Market Efficiency, 2026, pp 171-189 from Springer

Abstract: Abstract Previous chapters have shown that well-known asset pricing models published in top tier finance journals do a poor job of explaining anomaly portfolio returns. In stark contrast, a recent but lesser known model dubbed the ZCAPM by Kolari, Liu, and Huang (2021) almost completely explains anomaly stock returns. These findings call into question the validity of prominent asset pricing models. That is, commonly used multifactor models appear to be missing factors that are needed to explain anomaly returns. To test this possibility, in this chapter we employ a new out-of-sample cross-sectional regression coefficient test of alpha mispricing error terms. According to Jensen (1968), the alpha parameter in the estimation of a time-series regression for an asset pricing model measures mispricing error which arises primarily due to missing factors in the model. Many authors test for the presence of mispricing errorsMispricing error using the Gibbons, Ross, and Shanken (GRS) (1989) test for the joint zero equality of alphas across a sample of test assets (e.g., stock portfolios). Notably, this test is restricted to linear model tests on an in-sample basis. Extending the GRS testGibbons, Ross, and Shanken (GRS) tes of alphas, a recent study by KolariKolari, J.W., HuangHuang, J.Z., Liu, and LiaoLiao, H. (2014) proposed a novel out-of-sample alpha testAlpha test. More specifically, alphaAlpha parameters for tests assets estimated by a time-series regressionTime-series regression model are used as a factor loadingFactor loading in a standard out-of-sample (one-month-ahead) FamaFama, E.F. and MacBethMacBeth, J.D. (1973) cross-sectional regressionCross-sectional regression. If the alpha loading is significant, it means that missing factorsMissing factorsFactors exist in the time-series regressionTime-series regression asset pricing modelAsset pricing model. KolariKolari, J.W. et al. found that, even if in-sample GRS testsGibbons, Ross, and Shanken (GRS) tes indicate that alphas are jointly zero with no apparent mispricing errorMispricing error and missing factorsMissing factorsFactors, out-of-sample alpha testsAlpha test can suggest missing factorsMissing factorsFactors exist. In this chapter, we compare out-of-sample alpha testAlpha test results for the CAPMCAPM, prominent multifactor modelsMultifactor models, and the recent ZCAPMZCAPM. Our analyses use a variety of different test assets. Across these test asset samples, we find that mispricing errorsMispricing error are consistently lower in the ZCAPMZCAPM compared to other models. For most test assets, the ZCAPMZCAPM shows evidence of no missing factorsMissing factorsFactors. Thus, we conclude that the ZCAPM is not plagued by a missing factorMissing factors problem as in the case of the CAPMCAPM and popular multifactor modelsMultifactor models. By inference, while our evidence supports the ZCAPMZCAPM as a valid asset pricing modelValid asset pricing modelAsset pricing model, well-known multifactor modelsMultifactor models are not supported. Also, due to the ability of the ZCAPMZCAPM to well explain the cross-section of average stock returns, our empirical evidence suggests that the stock market is efficient.

Keywords: Alpha; Asset pricing models; Gibbons; Ross; and Shanken (GRS) test; Mispricing errors; Multifactor models; Out-of-sample cross-sectional regression test; ZCAPM; Valid asset pricing model (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-031-92901-4_7

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